Question

Use the summation formulas to rewrite the expression without the summation notation. Use the result to find the sums for n=10,100,1000 and 10,000

a. ∑ᶦ⁼ⁿᵢ₌₂ 2i+1/n²

Answer 1

The given summation expression simplifies to 2n². To find the sums for n=10, 100, 1000, and 10,000, apply the formula directly by substituting the respective values of n.

Step-by-step explanation:

The student asked to rewrite the expression ∑ᵢ⁾₁₀₀₀ 2i+1/n² without the summation notation and to find the sums for n=10, n=100, n=1000, and n=10,000. The sum inside the expression equates to n², as shown by distributing 2 and removing each successive (n-1), (n-3), etc., from the last and second to last terms respectively. To compute the sums for the given values of n, we can use the formula derived from the expression, which simplifies to 2n²